This sounds like it should be good motivation to build a version of J which uses some external bignum library.
I would expect more than a factor of 3 speed improvement for basic arithmetic. The trick, of course, is making sre that the result is correct -t that there are no circumstances where this change leads to a crash. Also realize that this would be a tradeoff. J's arbitrary precision (and rational) numbers are optimized for fast display, and that would be slower with something like gmp. Thanks, -- Raul On Thu, Oct 15, 2015 at 3:14 PM, Mike Day <[email protected]> wrote: > FYI, Project Euler problems 4, 36, 125, 486 involve > palindromic numbers. > > They're publicly available at > https://projecteuler.net/archives > > I think the earlier ones are quite straightforward. > 125 concerns palindromes that are the sums of consecutive > non-zero squares, such as 595 = +/*: 7 8 9 10 11 12 , and > is perhaps quite interesting. The problem is to sum all such > palindromes < 1e8. > > 486 has only been solved by 132 punters in the year since > it was first posted. As usual, the difficulty lies in obtaining > a solution for the given extreme problem size. It doesn't > really concern palindromic numbers, though, since they're > boolean, or members of a two-letter alphabet if you wish > to regard them as such. > > > "Palindrome-containing strings > > > Problem 486 > > Let F_5 (n) be the number of stringsssuch that: > > * sconsists only of '0's and '1's, > * shas length at mostn, and > * scontains a palindromic substring of length at least 5. > > For example, F_5 (4) = 0, F_5 (5) = 8, F_5 (6) = 42 and F_5 (11) = 3844. > > Let D(L) be the number of integersnsuch that 5 ≤ n ≤ Land F_5 (n) is > divisible by 87654321. > > For example, D(10^7 ) = 0 and D(5·10^9 ) = 51. > > Find D(10^18 ). > " > > My solution in J takes far too long, ~ 3 minutes, compared with > the stated Euler target of less than a minute. > > I have a Pari GP solution, too, but can't remember how to get it > to reproduce the result! > > Mike > > > > On 15/10/2015 18:02, Kip Murray wrote: >> >> Please read below. Forwarding is the only way I can get my awkward mailer >> to send you a message with copied material! --Kip Murray >> >> ---------- Forwarded message --------- >> From: km <[email protected]> >> Date: Thu, Oct 15, 2015 at 11:44 AM >> Subject: Finding prime palindromes >> To: Kip Murray <[email protected]> >> >> >> A prime palindrome is a prime which is unchanged when its decimal digits >> are reversed. Write verb find below. >> >> p: i.40 NB. first 41 primes >> 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 >> 103 107 109 113 127 131 137 139 149 151 157 163 167 173 >> >> find i.40 NB. palindromes among the first 41 primes >> 2 3 5 7 11 101 131 151 >> >> --Kip Murray >> >> Sent from my iPad >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > > > > --- > This email has been checked for viruses by Avast antivirus software. > https://www.avast.com/antivirus > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
